$\mathcal{N}=3$ Harmonic Super-Wilson Loop

TL;DR

This paper constructs supersymmetric Wilson loops in three-dimensional $ =3$ gauge theories using harmonic superspace, computes their expectation values at one loop, and compares with existing localization results to identify non-renormalized fermionic contributions.

Contribution

It introduces a supersymmetric generalization of Wilson loops in $ =3$ harmonic superspace and performs explicit one-loop calculations, extending previous $ =2$ results.

Findings

Constructed $ =3$ supersymmetric Wilson loops including $rac{1}{3}$-BPS and $rac{1}{6}$-BPS loops.

Performed one-loop vacuum expectation value calculations in superspace.

Identified fermionic contributions that do not receive subleading corrections.

Abstract

We study supersymmetric Wilson loops in $d=3$, $\mathcal{N}=3$ harmonic superspace, leading to a construction of a supersymmetrized generalization of the $\frac{1}{3}$-BPS Wilson loop for $\mathcal{N}=3$ gauge theories. This also includes a generalization of the $\frac{1}{6}$-BPS loop for ABJM theory. We perform a 'one-loop' computation of the vacuum expectation value of this operator directly in superspace and compare with the known $\mathcal{N}=2$ localization results at large $N$. This comparison also lets us identify certain fermionic contributions that do not receive any subleading corrections.